{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OQSZPG7KM3RPCEEFIHCYSIOLBJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"691ca47ece5fa8b07aaf7f55c9890f11fae633d69ff5cfad7c5271cf93b49742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:12:06Z","title_canon_sha256":"3ec8b7c258c15f4b685eec4381e8f1e01f36a20e278e6e719b6844367c9b5f38"},"schema_version":"1.0","source":{"id":"1612.09250","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09250","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09250v3","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09250","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"OQSZPG7KM3RP","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OQSZPG7KM3RPCEEF","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OQSZPG7K","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:25afc19a5710e5d497bc90d1175753c02ec0656fced28e2e8d55ac6c9e9a144a","target":"graph","created_at":"2026-05-18T00:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove universality of the Ghirlanda-Guerra identities and spin distributions in the mixed $p$-spin models. The assumption for the universality of the identities requires exactly that the coupling constants have zero means and finite variances, and the result applies to the Sherrington-Kirkpatrick model. As an application, we obtain weakly convergent universality of spin distributions in the generic $p$-spin models under the condition of two matching moments. In particular, certain identities for 3-overlaps and 4-overlaps under the Gaussian disorder follow. Under the stronger mode of total v","authors_text":"Yu-Ting Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:12:06Z","title":"Universality of Ghirlanda-Guerra identities and spin distributions in mixed $p$-spin models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09250","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:95cf5162a4b3e0ec6e4218c4979182dabcd7594c011c6347d08b75c734b275f3","target":"record","created_at":"2026-05-18T00:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"691ca47ece5fa8b07aaf7f55c9890f11fae633d69ff5cfad7c5271cf93b49742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:12:06Z","title_canon_sha256":"3ec8b7c258c15f4b685eec4381e8f1e01f36a20e278e6e719b6844367c9b5f38"},"schema_version":"1.0","source":{"id":"1612.09250","kind":"arxiv","version":3}},"canonical_sha256":"7425979bea66e2f1108541c58921cb0a59211dc7ff889824ad6b6be0c181f659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7425979bea66e2f1108541c58921cb0a59211dc7ff889824ad6b6be0c181f659","first_computed_at":"2026-05-18T00:22:06.471656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:06.471656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azRt2A8FcfqjSeCF+rVE9fh8dB+l+hPlw7cDQU3QtodVSW8XyLyrgR/t0pPDbgBO/94eoZy2bUfZ48JDI9cpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:06.472341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09250","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95cf5162a4b3e0ec6e4218c4979182dabcd7594c011c6347d08b75c734b275f3","sha256:25afc19a5710e5d497bc90d1175753c02ec0656fced28e2e8d55ac6c9e9a144a"],"state_sha256":"ef87fbf8372fefdf35291d41a583fb3521a5adbf15f6c393f7df2b97401b7fa8"}